The former Wolfsburg director is expected to join his fellow German Jurgen Klopp on a short-term deal ahead of a crucial summer transfer window.
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The Athletic reports that the Reds have already laid the groundwork for a big summer of change, but want to have Schmadtke in place in time for incumbent Julian Ward to depart.
Before leaving Wolfsburg in January, the 59-year-old former goalkeeper held similar roles at Hamburg and FC Cologne.
Speaking about the appointment, Klopp said: "If it happens, it would not be a Jurgen Klopp signing because we are both German or both know each other. That would have nothing to do with it. I can say that.
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"Jorg Schmadtke I have known a long, long time. He knows me probably not as long as I know him, because he was a much better player.
"But we started our second career at a similar moment. I became a coach at Mainz and he became sporting director at Aachen. Two teams of similar status, so from there we know each other a little bit.
"I know he is a good guy and a smart guy. Very good at what he did in Germany, definitely, very successful. His character is good, his personality is good, his humour is good. I know that from a few moments next to the pitch.
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Comparing him to former Borussia Dortmund director Michael Zorc, Klopp said: "Similar age group, similar situation, just a bit longer in retirement. There are some good sporting directors in Germany you wouldn't believe."
Before their final home game of the season, Liverpool announced the departures of Roberto Firmino, James Milner, Naby Keita and Alex Oxlade-Chamberlain.
With three of those players being midfielders, the Reds are expected to bring in two-to-three new recruits in the middle of the park, having pulled out of the race for Jude Bellingham to do so.